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2015
Towards Constraints on the Epoch of Reionization: A Phenomenological Approach
Matthew Malloy University of Pennsylvania, [email protected]
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Recommended Citation Malloy, Matthew, "Towards Constraints on the Epoch of Reionization: A Phenomenological Approach" (2015). Publicly Accessible Penn Dissertations. 1875. https://repository.upenn.edu/edissertations/1875
This paper is posted at ScholarlyCommons. https://repository.upenn.edu/edissertations/1875 For more information, please contact [email protected]. Towards Constraints on the Epoch of Reionization: A Phenomenological Approach
Abstract Based on observations of the early Universe, we know that shortly after the Big Bang, the Universe was composed almost entirely of neutral hydrogen and neutral helium. However, observations of nearby quasars suggest that the gas between galaxies today is neutral to less than one part in 10^4. Thus, it must be the case that some process occurred that stripped the electrons from almost all atoms in the intergalactic medium. Understanding the timing and nature of this process, dubbed ``reionization'', is one of the great outstanding problems in astrophysics and cosmology today. In this thesis, we develop several methods for utilizing existing and future measurements in order to make progress toward this end.
We begin by proposing two novel approaches for searching for signatures of underlying neutral hydrogen in the Lya and Lyb forest of distant quasars. We show that, if the Universe is >5% neutral at z ~ 5.5, then damping-wing absorption from neutral hydrogen and absorption from primordial deuterium should leave observable imprints in the Lya and Lyb forest, respectively. Furthermore, the presence of neutral islands should qualitatively alter the size distribution of absorbed regions.
We continue by discussing the ability for the intergalactic medium to retain a thermal memory of the reionization process at redshifts z ~ 5, which in turn affects the small-scale structure in the Lya forest. Motivated by this, we model the temperature of the intergalactic medium after reionization and develop a temperature measurement technique that should be able to distinguish between scenarios where reionization ends at z ~ 6 and at z ~ 10.
Lastly, we turn our attention to 21-cm observations during reionization. We demonstrate that, while precise mapping of 21-cm emission from neutral hydrogen should be infeasible by first and second generation interferometers, it may be possible to make crude maps of the reionization process and identify individual ionized regions. This would provide us with direct confirmation that we are observing reionization and provide information regarding its timing and the nature of the ionizing sources.
Degree Type Dissertation
Degree Name Doctor of Philosophy (PhD)
Graduate Group Physics & Astronomy
First Advisor Adam Lidz
Keywords 21-cm, Cosmology, Large Scale Structure, Lyman Alpha Forest, Reionization, Theory
Subject Categories Astrophysics and Astronomy | Physics
This dissertation is available at ScholarlyCommons: https://repository.upenn.edu/edissertations/1875 TOWARDS CONSTRAINTS ON THE EPOCH OF REIONIZATION:
A PHENOMENOLOGICAL APPROACH Matthew Malloy
A DISSERTATION in Physics and Astronomy Presented to the Faculties of the University of Pennsylvania in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy
2015
Supervisor of Dissertation Graduate Group Chairperson
Adam Lidz Marija Drndi`c Professor, Physics and Astronomy Professor, Physics and Astronomy
Dissertation Comittee:
James Aguirre, Assistant Professor, Physics and Astronomy Cullen Blake, Assistant Professor, Physics and Astronomy Elliot Lipeles, Professor, Physics and Astronomy Masao Sako, Professor, Physics and Astronomy TOWARDS CONSTRAINTS ON THE EPOCH OF REIONIZATION:
A PHENOMENOLOGICAL APPROACH
COPYRIGHT c
2015
Matthew Malloy
This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 4.0 License. To view a copy of this license, visit http://creativecommons.org/licenses/by-nc-sa/4.0/ To JM
iii Acknowledgements
This thesis truly would not have been possible without a great number of people. First and foremost, I would like to thank my advisor, Adam Lidz, whose endless ability to find interesting and important problems made this an exciting and rewarding experience and whose approach toward tackling those problems has invaluably and irreversibly affected my own. I could not have asked for a better advisor. I would also like to thank collaborators Judd Bowman and Piyanat “Boom” Kittiwisit at ASU, who gave me a greater appreciation for things on the experimental side, and also Andrei Mesinger, Ian McGreer, and Valentina D’Odorico. During my time at Penn, I benefited immensely from conversations and time spent with Garrett Goon and Rami Vanguri. Additionally, I would like to thank the Machine Learning Club and Alan Meert, who taught me literally half of what I have learned in the last year. Ross Anderson, Devin Kennedy, and Miles Wheeler – your inexplicable eagerness to contribute with algorithmic consults was both helpful and touching. I would also like to thank Jessie Taylor for valuable and interesting discussions. I am very fortunate to have been in Philadelphia at the same time as Caitlin Beecham, Chris Bryan, Tom Caldwell, Susan Fowler, Donnie Galvano, Bennet Huber, Andrew Mc- Carthy, Tom Pacific, Doug Schaefer, Katie Schmaling Meert, Elizabeth Stokes, Biquan Su, Debra Van Camp, and Haotian Xian, who, among many other things, played an essential role in me maintaining my sanity. I would also like to thank my parents and my sister who have been a constant source of love and support from the very beginning. Last, but not least, I would like to thank Dingding Jia for her unwavering support and encouragement.
iv ABSTRACT
TOWARDS CONSTRAINTS ON THE EPOCH OF REIONIZATION: A PHENOMENOLOGICAL APPROACH Matthew Malloy Adam Lidz
Based on observations of the early Universe, we know that shortly after the Big Bang, the Universe was composed almost entirely of neutral hydrogen and neutral helium. However, observations of nearby quasars suggest that the gas between galaxies today is neutral to less than one part in 104. Thus, it must be the case that some process occurred that stripped the electrons from almost all atoms in the intergalactic medium. Understanding the timing and nature of this process, dubbed “reionization”, is one of the great outstanding problems in astrophysics and cosmology today. In this thesis, we develop several methods for utilizing existing and future measurements in order to make progress toward this end. We begin by proposing two novel approaches for searching for signatures of underlying neutral hydrogen in the Ly α and Ly β forest of distant quasars. We show that, if the Universe is & 5% neutral at z 5.5, then damping-wing absorption from neutral hydrogen ∼ and absorption from primordial deuterium should leave observable imprints in the Ly α and Ly β forest, respectively. Furthermore, the presence of neutral islands should qualitatively alter the size distribution of absorbed regions. We continue by discussing the ability for the intergalactic medium to retain a thermal memory of the reionization process at redshifts z 5, which in turn affects the small- ∼ scale structure in the Ly α forest. Motivated by this, we model the temperature of the intergalactic medium after reionization and develop a temperature measurement technique that should be able to distinguish between scenarios where reionization ends at z 6 and ∼ at z 10. ∼
v Lastly, we turn our attention to 21-cm observations during reionization. We demonstrate that, while precise mapping of 21-cm emission from neutral hydrogen should be infeasible by first and second generation interferometers, it may be possible to make crude maps of the reionization process and identify individual ionized regions. This would provide us with direct confirmation that we are observing reionization and provide information regarding its timing and the nature of the ionizing sources.
vi Contents
Title i
Copyright ii
Dedication iii
Acknowledgements iv
Abstract v
Contents vii
List of Tables xi
List of Figures xii
1 First Things First 1 1.1 CosmicContext...... 1 1.2 TheShouldersofGiants ...... 7 1.2.1 The Ly α Forest ...... 7
1.2.1.1 Evolution of τeff ...... 14 1.2.1.2 Dark Pixel Covering Fraction ...... 20 1.2.1.3 Damping Wing Redward of Ly α ...... 24
vii CONTENTS
1.2.1.4 IGMTemperature ...... 30 1.2.2 The21-cmLine...... 37 1.2.2.1 The Intensity of the 21-cm Line ...... 38 1.2.2.2 21-cm Fluctuations with Interferometers ...... 44 1.2.2.3 Brief Description of 21-cm Interferometric Experiments . . 54 1.2.2.4 The Global 21-cm Signal ...... 60 1.2.3 The Cosmic Microwave Background ...... 65
1.2.3.1 Thomson Scattering Optical Depth, τe ...... 66 1.2.3.2 Kinetic Sunyaev-Zel’dovich Effect ...... 70 1.2.4 Ly α Emitters...... 72 1.2.4.1 Clustering of Ly α Emitters...... 72 1.2.4.2 Ly α EmitterFraction ...... 75 1.2.5 Luminosity Function Measurements ...... 76 1.3 MovingForward ...... 80
2 How to Search for Islands of Neutral Hydrogen in the z 5.5 IGM 82 ∼ 2.1 Introduction...... 82 2.2 Viability of Transmission Through a Partially Neutral IGM ...... 86 2.3 SimulationsandMockSpectra ...... 89 2.4 DarkGapStatistics ...... 94 2.5 StackingToySpectra...... 97 2.5.1 HIDampingWing ...... 98 2.5.2 Deuterium...... 101 2.6 StepsofApproach ...... 104 2.7 Results...... 107 2.7.1 Detecting the Damping Wing ...... 108 2.7.2 DeuteriumFeatureResults ...... 111 2.7.3 DarkGapStatistics ...... 115
viii CONTENTS
2.8 Forecasts ...... 116 2.8.1 Deuterium...... 117 2.8.2 HIDampingWing ...... 118 2.9 Conclusion ...... 119
3 Preliminary Stacking Results 135
4 On Modelling and Measuring the Temperature of the z 5 IGM 143 ∼ 4.1 Introduction...... 143 4.2 Simulations ...... 146 4.3 Reionization Histories ...... 147 4.4 TheThermalStateoftheIGM ...... 153 4.4.1 ModelingtheThermalState ...... 155 4.4.2 Simulated Temperature Field ...... 158 4.4.3 Variations around Fiducial Parameters ...... 167 4.5 Measuring the Temperature of the z 5IGM...... 169 ∼ 4.5.1 Hydrodynamic Simulations: Perfect Temperate-Density Relation Mod- els ...... 172 4.5.2 Degeneracy with the Mean Transmitted Flux ...... 174 4.5.3 Wavelet Amplitude PDFs in Inhomogeneous Reionization Models . . 177 4.5.4 Forecasts ...... 181 4.6 Conclusions ...... 185
5 Identifying Ionized Regions in Noisy Redshifted 21-cm Observations 199 5.1 Introduction...... 199 5.2 Method ...... 202 5.2.1 The21cmSignal...... 202 5.2.2 Semi-Numeric Simulations ...... 203 5.2.3 Redshifted 21 cm Surveys and Thermal Noise ...... 204
ix CONTENTS
5.2.4 Foregrounds...... 207 5.3 ProspectsforImaging ...... 208 5.3.1 TheWienerFilter ...... 208 5.3.2 Application to a Simulated 21 cm Signal ...... 212 5.4 Prospects for Identifying Ionized Regions ...... 213 5.4.1 The Optimal Matched Filter ...... 214 5.4.2 Application to Isolated Spherical Ionized Regions with Noise . . . . 215 5.4.3 Application to a Simulated 21 cm Signal ...... 218 5.4.4 Success of Detecting Ionized Regions ...... 222 5.4.5 Range of Template Radius Considered ...... 224 5.5 Variations on the Fiducial Model ...... 226 5.5.1 IonizedFraction ...... 226 5.5.2 TimingofReionization...... 228 5.5.3 Effects of Foreground Cleaning ...... 229 5.5.4 128 Antenna Tile Configurations ...... 230 5.6 Favorable Antenna Configurations for Bubble Detection ...... 231 5.7 ComparisonstoPreviousWork ...... 233 5.8 Conclusion ...... 234
6 Conclusion 248
Glossary 252
References 256
x List of Tables
3.1 Overview of quasar spectra used in our preliminary stacking tests...... 136
xi List of Figures
1.1 Milestones in the evolution of the Universe from the Big Bang to today.(Photo fromNASAWMAPscienceteam) ...... 3 1.2 Slices through numerical simulations of reionization. The above panels are simulation outputs from McQuinn et al. (109) showing four different reion- ization models. Neutral regions are shown in black and ionized regions are shown in white. Each row is at fixed x with x = 0.8 (top), 0.5 (mid- h HIi h HIi dle), 0.3 (bottom). The luminosities of the ionizing sources are related to their mass by N˙ m1/3 (left), N˙ m (left-middle), N˙ m5/3 (right- ∝ ∝ ∝ middle), and N˙ m but with a larger minimum mass (right). Each slice has ∝ a sidelength of L =93Mpc...... 6 1.3 Illustration of the basic physics behind the Ly α forest and how gas at dif- ferent locations along the line of sight results in absorption lines at different wavelengths. (Image from http://www.astro.ucla.edu/)...... 12 1.4 Flux as a function of rest-frame wavelength for a quasar at z = 0.158 (top) and z = 3.62 (bottom). The denser IGM at higher z results in a dense “forest” of absorption lines blueward of the rest-frame Ly α line (1216A)˚ in the lower panel. (Image from http://www.astro.ucla.edu/)...... 13
xii LIST OF FIGURES
1.5 The inferred evolution of the photoionization rate, ΓHI (left), and neutral fraction (right) from Fan et al. (50). In the left-hand panel, measurements of the effective optical depth in the Ly α (blue), Ly β (green), and Lyγ (ma- genta) forest are converted to estimates of the photoionization rate, with arrows indicating upper bounds. The small circles are measurements in in- dividual redshift bins over the 19 quasars used with the large circles being averages. In the right-hand panel, measurements of the photoionization rate are converted to estimates of the volume-averaged neutral fraction. . . . . 18 1.6 Current limits on x derived from the dark-pixel covering fraction in Mc- h HIi Greer et al. (104). Lightly-shaded points are older limits obtained in McGreer etal.(105)...... 23 1.7 Quasar ULAS J1120+0641 identified at redshift z = 7.085 along with several fitsforthedampingwing...... 27 1.8 Spectrum of GRB140515A, a gamma-ray burst located at z = 6.33. The right-hand panel overlays damping wing models from a host absorber (blue), a pure IGM model with x = 0.056 (red), and a combination model h HIi (green). The authors argue that, while each curve provides an equally-good fit to the data, the sharp rise in transmission shown is inconsistent with a significantly-neutralIGM...... 29 1.9 Schematic representation of Doppler broadening. The HI atom is moving away with velocity v from incoming radiation with frequency ν. The observed frequency of the radiation in the atom’s rest frame is ν(1 ξ/c) where ξ is − the component of the velocity parallel with the incident radiation...... 35
xiii LIST OF FIGURES
1.10 Measuring the temperature of the IGM in z & 6 quasar proximity zones. This figure shows mock spectra, and corresponding simulated IGM properties, from Bolton et al. (18) in the top four panels. The bottom panel shows the observed spectrum from SDSS J0818+1722, which Bolton et al. (18) use in order to make temperature measurements inside the proximity zone. Dashed lines indicate regions where Voigt-profile fitting was performed and downward arrows indicate the detected centers of the Voigt profiles...... 36 1.11 Schematic representation of the 21-cm transition where the transition be- tween aligned spins of the proton and electron to anti-aligned spins results in the emission of a photon with λ =21cm...... 42 1.12 Simulation cube of the 21-cm signal during reionization (top-left) along with simulated noise for an interferometer (top-right) and the galactic foregrounds (bottom). This figure demonstrates that, while the sources of noise are sev- eral orders of magnitude larger than the signal, these three contributions to observations are dominant on different scales. The volume of each cube is 1 (Gpc/h)3. In this figure, the line of sight direction away from the observer is to the right and slightly out of the page...... 43 1.13 Depiction of the extra path length, ∆ℓ, of radiation (dot-dashed lines) in- cident on two elements (solid black rectangles) in an array separated by ~r when considering a position on the sky θˆ...... 51
xiv LIST OF FIGURES
1.14 Percentage of pixels “imaged” (SNR > 1) as a function of wavemode, k for the MWA (dashed), LOFAR (dot-dashed), and the SKA (solid). The vertical hatched line shows the distance scale above which (smaller k) the residuals from foreground subtraction are expected to dominate the 21-cm signal. This demonstrates that, for first-generation 21-cm experiments, a very small frac-
tion of pixels with k > khatched will be “imaged”. This estimate assumes that fluctuations in the 21-cm signal are driven from density fluctuations rather than fluctuations in the ionization field, so it is somewhat conservative. Taken fromMcQuinnetal.(113)...... 52 1.15 The redshift evolution of the 21-cm power spectrum in simulated models of reionization. The left panel shows the evolution of the power spectrum during reionization for the fiducial reionization model in Lidz et al. (90). We can see that, as reionization progresses, the slope of the power spectrum in the k-mode range accessible to interferometers (0.1 h/Mpc k 1 h/Mpc) ≤ ≤ declines. The amplitude of this part of the power spectrum peaks around x = 0.5. The right-hand panel shows the evolution of the power spectrum h HIi slope (top) and magnitude (bottom) during reionization for a few different reionization models. This demonstrates that the general power-spectrum evolution described is generic to many reionization models. Both figures are takenfromLidzetal.(90)...... 53 1.16 Several antennae in the GMRT core. www.mso.anu.edu.au ...... 54 1.17 A highly-redundant configuration of tiles for the PAPER interferometer, well- suited for power-spectrum measurements. Picture from www.discovermagazine.com ...... 55 1.18 Several antenna elements in the core of the MWA array. Image taken from www.mwatelescope.org/multimedia...... 56 1.19 Planned layout of the HERA interferometer. Image taken from (45). . . . . 58
xv LIST OF FIGURES
1.20 The central antenna stations for the LOFAR interferometer. Image taken from www.astron.nl...... 59 1.21 An artists impression of what the reionization-focused element of the SKA might look like. “SKA sparse array big” by SKA Project Development Office and Swinburne Astronomy Productions - Swinburne Astronomy Productions for SKA Project Development Office. Licensed under CC BY-SA 3.0 via WikimediaCommons...... 59 1.22 Schematic representation of the 21-cm signal. The top panel shows a plausible signal for 21-cm fluctuations from shortly after the big bang (left) to today (right). Blue indicates the signal is seen in absorption and red indicates it is seen in emission. In the bottom panel, the strength and sign of the averaged signal is shown along with several important landmarks coinciding with the turning points in this curve. The redshift is shown at the top of the bottom panel. The precise timing of the turning points is not well- constrained, this is just one plausible history. As such, the exact redshift values do not completely match those that we described in the text. Figure takenfrom(147)...... 63 1.23 An illustration (Wayne Hu, http://background.uchicago.edu/ whu/) of how a net polarization signal is generated from Thomson scattering due to the presence of a quadrupole anisotropy. The blue cross and red cross show relatively strong and weak incident radiation, respectively, on an electron at the origin. The red/blue cross indicates the average polarization of scattered light and demonstrates that it obtains a net vertical polarization...... 69
xvi LIST OF FIGURES
1.24 The (simulated) effect of the neutral fraction on the observed clustering of LAEs (taken from McQuinn et al. 108). The top panels show the underly- ing ionization fields, the middle row shows the true location of LAEs in the simulation, and the bottom panel shows the detectable LAEs in the simula- tion. This shows that, LAEs which occupy the same ionized bubble will be observable, resulting in a less homogeneous field of observable LAEs. Each panelis94Mpcacross...... 74 1.25 Several claimed constraints on x during the Epoch of Reionization (mark- h HIi ers), most of which we touch on in this section, along with best fit curves calculated using luminosity functions (Robertson et al. 154). The red shaded curve shows the maximum-likelihood model of the neutral fraction (white)
with 1σ errors and is consistent with Planck τe measurements. The analo- gous curve for Robertson et al. (155) is shown in blue, but is in conflict with
the WMAP τe constraints. A model that forces the blue curve to satisfy
the WMAP τe constraint is shown in yellow. This figure demonstrates that, under some assumptions, the scenario where galaxies dominate reionization is not in conflict with the constraints on the timing of the EoR to date. . . 79
2.1 Example mock Ly α forest spectrum and corresponding neutral fraction. The top panel shows the Ly α transmission while the bottom panel is the neutral fraction along the line of sight, with ionized regions set to x 0 for illus- HI ≈ tration. The black curve in the top panel shows the transmission through the forest when absorption due to the hydrogen damping wing is neglected, while the red curve includes damping wing absorption. The comparison illustrates that damping wing absorption has a prominent impact, but it is also clear that the presence of the damping wing will be hard to discern by eye. The line of sight is extracted from a model with x = 0.22, but note that we h HIi have deliberately chosen a sightline with more neutral regions than typical. 94
xvii LIST OF FIGURES
2.2 Dark gap size distribution for the x = 0.22, F = 0.1 model. The solid h HIi h i blue curve shows the total distribution of dark gaps from an ensemble of mock spectra, where the magenta (cyan) curve shows the same thing but for the dark gaps sourced by ionized (neutral) gas. Here, we have focused on dark gaps with L> 0.75 Mpc/h. This clearly demonstrates that neutral hydrogen is the dominant source of large dark gaps in our mock spectra, provided there isanappreciableneutralfraction...... 97 2.3 Large-length tail of the dark gap size histogram for x = 0 (magenta), 0.05 h HIi (cyan), 0.22 (blue), and 0.35 (black) for the case when F = 0.1. The y-axis h i is scaled to indicate the expected number of dark gaps obtainable from 20 spectra. Bins in this figure are spaced logarithmically. The dashed magenta line indicates the dark-gap size distribution in the fully ionized case when the true transmission is F = 0.03, but continuum fitting errors result in a h i measured mean transmission of F = 0.1...... 98 h measi 2.4 Stacking idealized Ly α spectra containing toy HI regions. The above fig- ure shows the stacked transmission outside isolated HI regions with mean density and size L = 0.76 Mpc/h (v 100km/s), L = 1.27 Mpc/h ext ≈ (v 170km/s), and L = 5.34 Mpc/h (v 700km/s) shown in black, ext ≈ ext ≈ blue, and cyan, respectively. The solid red curve shows the stacked trans- mission outside of the same HI regions neglecting the damping wing, which will be the same on average in all cases. In generating these spectra, we as- sume F = 0.1. In this greatly-idealized case, the presence of the hydrogen h i damping wing is seen clearly through extended excess absorption compared to the red curve. Furthermore, we can see that the excess absorption closely follows what we would expect analytically based on multiplying Eq. 2.6 by the overall mean transmission. In this figure, all stacking starts at HI/HII boundaries...... 100
xviii LIST OF FIGURES
2.5 Presence of deuterium absorption revealed through stacking idealized Ly β spectra containing toy neutral regions. The red and black curves show the stacked Ly β transmission redward and blueward, respectively, of toy neutral regions of length L = 5 Mpc/h ( 700km/s) randomly inserted into many ≈ sightlines, with spectra generated assuming F = 0.1. In each case, h Lyαi stacking begins at the underlying HI/HII boundary. We have also mimicked the effect of including foreground Ly α absorption by scaling the feature by the mean transmission in the foreground Ly α forest. This demonstrates that, at least in this idealized case, the presence of deuterium absorption can be easily seen out to 80km/spasttheHI/HIIboundaries...... 104 ∼ 2.6 Ly α stacking results for various neutral fractions. The top panel shows the mean (noiseless) stacked transmission outside of large absorption systems (solid) and small absorption systems (dashed) in the Ly α forest for neutral fractions x = 0.35 (black), 0.22 (blue), 0.05 (red), and 0 (magenta). h HIi The transmission here is estimated from a large ensemble of mock spectra to obtain a smooth estimate of the average transmission around saturated regions in each model. The bottom panel shows the statistical significance of the difference between the dashed and solid curves in the top panel assuming a sample of 20 spectra are used in the stacking process...... 112 2.7 Ly α stacking results assuming F = 0.05. The above panels are identical h i to those in Fig. 2.6 except that mock spectra have been generated assuming F = 0.05...... 113 h i 2.8 Results of Ly α stacking with HIRES-style spectra ( F = 0.1). The above h i panel is identical to the bottom panel in Fig. 2.6 except that the spectra have had the bin size and spectral resolution adjusted to match that of Keck- HIRES spectra. Additionally, we have added noise such that the spectra have a signal-to-noise value of 10 per pixel at the continuum...... 114
xix LIST OF FIGURES
2.9 Deuterium Ly β stacking results for various neutral fractions. The top panel shows the mean ensemble-averaged noiseless stacked transmission moving blueward (solid) and redward (dashed) away from large absorption systems in the Ly β forest for neutral fractions x = 0.35 (black), 0.22 (blue), h HIi 0.05 (cyan), and 0 (magenta). The bottom panel shows the excess blue- ward absorption in units of the standard deviation of the stacked redward transmission,assuming20spectra...... 131 2.10 Results of Ly β stacking with HIRES-style spectra. The above panel is the same as in the bottom panel of Fig. 2.9, except that it is generated using HIRES-style spectra, with spectral resolution of FWHM = 6.7km/s and additive noise with signal to noise of 30 per 2.1 km/s pixel at the continuum. 132 2.11 Mock dark gap size distribution. This figure is identical to Fig. 2.3 except that it uses spectra with spectral resolution FWHM = 100km/s, bin size
∆vbin = 50km/s, and a signal-to-noise ratio of 10 at the continuum. This figure shows the expected histogram of dark gap sizes using 20 spectra with x = 0.35 (black), 0.22 (blue), 0.05 (cyan), and 0 (magenta) at fixed h HIi F = 0.1...... 132 h i
xx LIST OF FIGURES
2.12 Using the Ly β forest to estimate damping-wing-less Ly α transmission. The above figure shows the estimated shape of stacked damping wing absorption for x = 0 (magenta), 0.05 (cyan), 0.22 (blue), and 0.35 (black). The h HIi curves have been normalized to have their mean values peak at 1. Addi- tionally, we show error bars for the fully ionized case and x = 0.35 case h HIi which indicate the scatter in the curves between groups of 20 spectra. The top plot is obtained by using a large ensemble of mock spectra to model a mapping between stacked Ly β transmission and stacked damping-wing-less Ly α transmission and then applying this to groups of 20 spectra. Meanwhile, the bottom figure plots the ratio of the stacked Ly α flux to the stacked Ly β flux, providing a simplified estimate of the damping wing contribution to the absorptionforeachcase...... 133 2.13 Model for the extended damping wing absorption. The left panel shows the components of our model for stacked transmission outside of a neutral re- gion compared to the stacked transmission using mocked spectra (magenta) for x = 0.22. We show the absorption due to the central neutral re- h HIi gion (blue), average absorption due to neighboring, clustered neutral regions (cyan), and the product of the two transmissions (black). These are denoted in the legend as “1-Halo”, “2-Halo”, and “1-Halo + 2-Halo” in analogy with the halo model. In the right-hand panel, we show the comparison between the modelled transmission (dashed) and transmission from stacked mocked spectra (solid) for x = 0.35 (black), 0.22 (blue), and 0.05 (cyan). The h HIi curves in the right-hand figure have been multiplied by the mean transmis- sion (computed here ignoring resonant absorption for illustration). In this appendix, the stacking is done at the HI/HII boundaries and only damping wing absorption is incorporated to demonstrate the extended excess absorp- tion owing to correlated neighboring systems...... 134
xxi LIST OF FIGURES
3.1 The above figure shows the results of stacking Ly α transmission outside of dark gaps in the Ly β portion of the spectrum with L< 300km/s (top) and L > 300km/s (bottom) for dark gaps with 5.5 z 5.7. The solid ≤ gap ≤ curves are generated using mock spectra assuming x = 0 (magenta), h HIi 0.05 (cyan), 0.22 (blue), and 0.35 (black). The dashed green line shows the stacking results for the spectra described in Table 3.1...... 139 3.2 This figure is identical to Fig. 3.1 except we stack outside of dark gaps with 5.7 z 6...... 140 ≤ gap ≤ 3.3 This figure shows the results of stacking Ly β transmission outside of dark gaps with L> 100km/s in the spectra described in Table 3.1. For this figure, we stack outside of dark gaps with 5.5 z 5.7...... 142 ≤ gap ≤ 3.4 This figure is identical to Fig. 3.3 except we stack outside of dark gaps with 5.7 z 6...... 142 ≤ gap ≤ 4.1 Example reionization histories. The red triangles show the simulated volume- average ionization fraction in our semi-numeric High-z reionization model, the black squares are for the Mid-z reionization scenario, and the blue pentagons are for a low redshift (Low-z) reionization model. The black dashed line shows the reionization history computed by solving Eq. 4.1 with ζ = 46, 9 Mmin = 10 M⊙ and C = 3. The semi-numeric efficiency parameters ζ˜(z) in the Mid-z case have been tuned to match this model...... 151
xxii LIST OF FIGURES
4.2 Thermal state of gas elements with a given reionization redshift, as a function of that redshift. In each case, the gas elements are heated to a temperature of T = 2 104 K during reionization, and the residual photo-heating after r × reionization is computed assuming that the (hardened) spectral index of the ionizing sources is α = 1.5 near the HI photoionization edge. Top panel: The
temperature at mean density (T0) for gas elements at each of z = 4.5, 5.0 and 5.5 as a function of their reionization redshift. Bottom panel: This is similar to the top panel, except it shows the slope of the temperature-density relation (γ 1) rather than T . Note that although we assume that gas elements with − 0 a given reionization redshift all land on a well defined temperature-density relation, this will not generally be a good description once we account for the spread in reionization redshift across the universe...... 159 4.3 Reionization redshifts and temperatures at z = 5.5 in the low-z reionization model. Left panel: The reionization redshifts for a narrow slice (0.25 Mpc/h thick) through the simulation. Each slice is 130 Mpc/h on a side. The red regions indicate locations with the highest reionization redshifts across the simulation slice, while the dark regions are the last to be reionized. Right panel: The temperature of the same slice as in the top panel. The red areas in this panel show the hottest locations in the slice, and correspond to the dark regions in the top panel that are reionized late. The dark blue regions in the temperature slice, on the other hand, are the coolest regions that reionized first. The color scales are chosen so that 99% of simulation cells in the slice shown here have redshifts and temperatures falling between the minimum andmaximumvaluesonthecolorbar...... 160
xxiii LIST OF FIGURES
4.4 Reionization redshifts and temperatures at z = 5.5 in the high-z reionization model. Identical to Fig. 4.3, except this figure shows the contrasting High-z model. Note that the color scale in this case also encompasses 99% of the reionization redshifts and temperatures in the simulation slice, but that these ranges are different than in the previous figure...... 161 4.5 Temperature density relations at z = 4.5 and z = 5.5 in the Low-z reion- ization model. The blue points show the temperature and density of gas elements from the simulation at z = 5.5, while the black points are the same at z = 4.5. The red short dashed line shows the median simulated temper- ature as a function of density at z = 5.5. The green long dashed line is the same at z = 4.5...... 163 4.6 Temperature density relations at z = 4.5 and z = 5.5 in the High-z reioniza- tion model. Identical to Fig. 4.5, except the results here are for the High-z reionizationmodel...... 164 4.7 Power spectrum of temperature fluctuations in various models. The curves show the power spectrum of δ (x) = (T (x) T )/ T from the simulated T0 0 − h 0i h 0i models. The blue dotted line, the black solid line, and the red short-dashed line are the power spectra at z = 5.5 in the Low-z, Mid-z, and High-z models
respectively. The black long-dashed line shows the δT0 power spectrum at z = 4.5 in the Mid-z model to illustrate how the temperature fluctuations fadewithtime...... 166
xxiv LIST OF FIGURES
4.8 Thermal state at z = 5.5 for various reionization temperature and spectral shape models. This is similar to the z = 5.5 curves in Fig. 4.2, except here we
vary the reionization temperature, Tr, and the spectral shape, α. Increasing
Tr leads to a higher T0 and a flatter γ for recently reionized gas parcels,
while parcels that reionize at sufficiently high redshifts are insensitive to Tr. A harder ionizing spectrum after reionization (smaller α) leads mostly to a
slightly larger value of the asymptotic temperature achieved at high zr. The harder spectrum also slightly hastens the transition of γ to its asymptotic value...... 191 4.9 Temperature density relation at z = 5.5 for various reionization temperatures in the High-z and Low-z models. The “X”s in the legend indicate the color of the points in the corresponding models, while the dashed lines in the same models have different colors to promote visibility. The models in the legend are listed from top to bottom: the highest points and line (indicating the median temperature at various densities) show the T = 2 104 K, Low-z r × model; next is the T = 1 104 K, Low-z model; then the T = 3 104 K, r × r × High-z model; and finally the T = 3 104 K, High-z model...... 192 r × 4.10 Example sightlines and wavelet amplitudes for two different models of the IGM temperature at z 5. The top panel shows δ (x) for an example ∼ F sightlines with T = 2.5 104 K, γ = 1.3 (red dashed) and the same sightline 0 × except with T = 7.5 103 K, γ = 1.3 (black solid). The bottom panel 0 × shows the smoothed wavelet amplitudes, AL, along each spectrum. The lower temperature model has more small scale structure and larger wavelet
amplitudes. The smoothing scale sn = 51 km/s here, while ∆u = 3.2 km/s and L = 1, 000km/s...... 193
xxv LIST OF FIGURES
4.11 Probability distribution of A for various T models at z 5. Each model L 0 ∼ here assumes a perfect temperature density relation with γ = 1.3, and in each case the mean transmitted flux has been fixed – by adjusting the intensity of the ionizing background – to F = 0.20. As in Fig. 4.10, the smoothing h αi scale has been set to sn = 51 km/s, while ∆u = 3.2 km/s and L = 1, 000 km/s...... 194 4.12 Degeneracy with F . Left panel: Although the PDF of A is sensitive to h i L T , this effect is degenerate with the impact of varying F . For instance, 0 h i the model with T = 1.5 104 K and F = 0.20 is closely mimicked by 0 × h i a colder model with T = 7.5 103 K, yet a larger mean transmission of 0 × F = 0.30. Right panel: This illustrates that the degeneracy can be broken h i by measuring the (relatively) large scale flux power spectrum. The curves here show the flux power spectrum, evaluated at a single convenient (larger- scale) wavenumber of k = 0.003 s/km, in each T model as a function of F . 0 h i The triangle and pentagon show the flux power for each model at the F for h i which the wavelet amplitude PDFs are degenerate in the two models. The large scale flux power in these two models differs appreciably and can be used to break the degeneracy. The red dotted and black dotted horizontal lines areintendedonlytoguidetheeye...... 195
xxvi LIST OF FIGURES
4.13 Example sightlines and wavelet amplitudes from the Low-z and High-z reion- ization models. In the models here, the global mean flux is F = 0.1 and h i z = 5.5. In each panel the red dotted line shows a sightline through the T = 3 104 K, Low-z reionization model while the black solid line is the r × same sightline, except in this case the temperature field is drawn from the High-z reionization model (with T = 2 104 K). The simulated density and r × temperature fields have small scale structure added according to the lognor- mal model, as described in the text. Top panel: The simulated temperature
field. Middle panel: The transmission field, δF . Bottom panel: The smoothed
wavelet amplitude with L = 1, 000 km/s, sn = 34 km/s, and ∆u = 2.1 km/s. The transmission fluctuations and wavelet amplitudes are larger than in Fig. 4.10, mostly because of the lower mean transmitted flux adopted here. . . . 196
4.14 Probability distribution of AL for various reionization and temperature mod- els at z = 5.5. Left panel: In this panel all models are normalized to F = 0.2. The solid black curve shows the wavelet amplitudes for the h i High-z reionization model (with T = 2 104 K), while the red dotted and r × blue dashed curves show Low-z reionization models with reionization tem- peratures of T = 2 104 K and T = 3 104 K respectively. The magenta r × r × dot-dashed line shows a homogeneous temperature model for comparison. In this case, the temperature was set to match the median temperature in the Low-z, T = 3 104 K model for gas at the cosmic mean density; the broader r × distribution in the Low-z model reflects the impact of inhomogeneous reion- ization. Right panel: Identical to the top panel, but here the models fix F = 0.1. In each case, the filter scale and pixel size are set to s = 34 km/s h i n and ∆u = 2.1 km/s respectively, while L = 1, 000km/s...... 197
xxvii LIST OF FIGURES
4.15 Heating/cooling rates at z 7. Left panel: The (absolute value of) the rates ∼ for relevant processes in the IGM at T = 104 K as a function of density, assuming that hydrogen is highly ionized and that helium is mostly singly- ionized. Right panel: Similar to the left panel except the rates are shown as a function of temperature for gas at the comic mean density...... 198
5.1 Fourier profile of the Wiener filter, W (k). The filter is averaged over line-of-
sight angle and the results are shown at zfid = 6.9 for simulated models with x = 0.51 (blue dotted), x = 0.68 (cyan dot-dashed), x = 0.79 (green h ii h ii h ii dashed), and x = 0.89(redsolid)...... 211 h ii 5.2 Application of the Wiener filter to simulated data. The results are for our fiducial model with x = 0.79 at z = 6.9. Top-Left: Spatial slice of the h ii fid unfiltered and noise-less 21 cm brightness temperature contrast field (nor-
malized by T0). Top-Right: Simulated signal-to-noise field after applying the Wiener filter to a pure noise field. Bottom-Left: Simulated signal-to- noise field after applying the Wiener filter to the noisy signal. This can be compared with the uncorrupted input signal shown in the top-left panel and the noise realization in the top-right panel. Bottom-Right: Simulated signal- to-noise field after applying the Wiener filter to the noiseless signal. (The filtered noiseless signal shown here is normalized by the standard deviation of the noise to facilitate comparison with the other panels.) All panels show a square section of the MWA field of view transverse to the line of sight with sidelength L = 1 h−1 Gpc . All slice thicknesses are 8 h−1 Mpc . Unless ∼ noted otherwise, the simulation slices in subsequent figures have these same dimensions...... 237
xxviii LIST OF FIGURES
5.3 Impact of foreground cleaning on the Wiener-filtered field. The top slice is a perpendicular, zoomed-in view of the simulated, unfiltered, noise-less brightness temperature contrast. The bottom slice is the signal-to-noise of the same region after applying the Wiener filter to the noisy signal field. The vertical axis shows the line-of-sight direction, with its extent set to the −1 distance scale for foreground removal, Lfg = 185 h Mpc . The horizontal axis shows a dimension transverse to the line of sight and extends 1 h−1 Gpc...... 238 5.4 Expected signal-to-noise ratio at the center of isolated, spherical, ionized bubbles as a function of bubble radius after applying the optimal matched
filter. The curves show the signal-to-noise ratio at zfid = 6.9 for the MWA- 500 at various neutral fractions: x = 0.4 (blue solid), 0.3 (cyan dashed), h HIi and 0.2 (green dot-dashed). For contrast, the red dotted curve indicates the expected signal-to-noise for an interferometer with a field of view and collecting area similar to a 32-tile LOFAR-like antenna array (at x = 0.4)...... 239 h HIi 5.5 Application of the matched filter to simulated data and noise ( x = 0.79 h ii −1 at zfid = 6.9). The template radius of the filter is 35 h Mpc , since this is a commonly detected bubble radius for our matched filter search. Top-Left: Spatial slice of the unfiltered and noise-less 21 cm brightness temperature contrast field. Top-Right: Simulated signal-to-noise field after applying the matched filter to a pure noise field. Bottom-Left: Simulated signal-to-noise field after applying the matched filter to the noisy signal. This can be com- pared directly to the top-left panel. Bottom-Right: Simulated signal-to-noise field after applying the matched filter to the noiseless signal. All panels are at the same spatial slice. See text for discussion on interpreting signal-to-noise values...... 240
xxix LIST OF FIGURES
5.6 Impact of foreground cleaning on the matched-filtered field. This is similar to Figure 5.3, except that the results here are for a matched filter with a −1 template radius of RT = 35 h Mpc...... 241 5.7 An example of a detected ionized region. Top-left: Signal-to-noise field after applying the matched filter to the noisy signal. The detected bubble is plotted on top of the corresponding region in the map. Top-Right: Zoomed-in view of the detected bubble in the matched-filtered map. Bottom-Left: Detected bubble superimposed on a zoomed-in view of the noise-less unfiltered 21 cm brightness temperature contrast map. Bottom-Right: A perpendicular zoomed-in view of the bubble depicted in the bottom-left panel. All matched- filtered maps use the template radius that minimizes the signal-to-noise at the center of the detected bubble. In the top-left case, the boxlength is L = 1 h−1 Gpc , while in the zoomed-in slices it is L 500 h−1 Mpc . . . . . 242 ≈ 5.8 An example of an ionized region that our algorithm detects as several neigh- boring bubbles. Top-left: Signal-to-noise field after applying the matched filter to the noisy signal. The main detected bubble is plotted on top of the corresponding region in the map. Top-Right: Zoomed-in view of the main de- tected bubble in the matched filtered map (solid curve) along with two other nearby detected bubbles (dashed curve). Bottom-Left: The detected bubble superimposed on the zoomed-in, noise-less, unfiltered 21 cm brightness tem- perature contrast map. Again, the additional nearby detected bubbles are shown (dashed curve). Bottom-Right: A perpendicular view of the bubble depicted in the bottom-left panel, with the nearby detected bubbles visible. All matched-filtered maps use the template radius that maximizes the sig- nal to noise at the center of the main detected bubble. The box length in the top-left figure is L = 1 h−1 Gpc , while in the zoomed-in panels, the box length is L = 550 h−1 Mpc...... 243
xxx LIST OF FIGURES
5.9 A measure of the bubble detection success rate. The points ( ) show the × volume-averaged ionized fraction of detected bubbles versus their detected radius. For comparison, the cyan shaded region shows the 1-σ spread in the ionized fraction of randomly placed bubbles of the same radii. The bubble depicted in Fig. 5.7 is marked with a large red square, while the three bubbles shown in Fig. 5.8 are marked with large green circles...... 244 5.10 Size distributions of detected bubbles for varying (volume-averaged) ion- ization fractions. The histograms show the size distribution of (identified) ionized regions for simulation snapshots with volume-averaged ionized frac- tions of x = 0.51 (top-left), 0.68 (top-right), 0.79 (bottom-left), and 0.89 h ii (bottom-right). These figures demonstrate how the total number and size distribution of detected bubbles varies with ionized fraction...... 245 5.11 Bubble detection with the MWA-128. This figure is similar to Figure 5.5, except it is for the MWA-128 configuration rather than for the MWA-500. . 246 5.12 Bubble detection with a LOFAR-style interferometer. This figure is similar to Figure 5.5, except it is for the LOFAR configuration rather than the MWA- 500. Additionally, all boxes in this figure have a side length of 426 h−1 Mpc , corresponding to the field-of-view of the LOFAR-style interferometer at z = 6.9...... 247
xxxi Chapter 1
First Things First
The subject of this thesis is the “Epoch of Reionization”, also known as “hydrogen reion- ization” or “reionization” or simply the “EoR”. Let us start in 1.1 with a brief description § of the reionization process, how it relates to the evolution of the Universe as a whole, and some of the open questions that this thesis aims to address. In 1.2, we will provide a brief § overview of the variety of probes that have been used to constrain reionization to date, while also providing motivation for the development of additional approaches in 1.3. From § there, we will move onto our own work. We begin by discussing several novel methods for utilizing the Ly α and Ly β forest, first to constrain the end of reionization in 2 and 3, and § § then to constrain the temperature of the intergalactic gas at slightly later times in 4. In 5, § § we will continue by developing approaches to directly observe the reionization process with interferometric experiments that will be up and running in the near future. We conclude in 6. §
1.1 Cosmic Context
The problem of reionization arises when trying to reconcile observations of the early Uni- verse with those of the present-day Universe. Namely, Big Bang nucleosynthesis implies
1 1.1 Cosmic Context
that the early Universe was composed almost entirely of hydrogen and helium and observa- tions of the Cosmic Microwave Background (CMB, discussed in 1.2.3) demonstrate that, § when the Universe was 380,000 years old,1 this hydrogen and helium became neutral. ∼ However, observations of nearby quasars (specifically, the Ly α forest, discussed in 1.2.1) § demonstrate that the gas between the galaxies, dubbed the intergalactic medium (IGM), is almost entirely ionized by at least & 1 billion years after the Big Bang to today (Gunn and Peterson 65).2 Therefore, some process – acting across the entire volume of intergalactic space in the intervening 13 billion years – must have managed to strip the electrons from ∼ almost all atoms, and keep them ionized even today. We refer to this process as the Epoch of Reionization. Technically, several ionizations have to take place: ionizing hydrogen, singly ionizing helium, and doubly ionizing helium with the required energies per ionization being 13.6 eV, 24.6 eV, and 54.4 eV, respectively. Since the first two processes require similar energies, they are thought to occur concurrently. However, the complete ionization of helium requires four times as much energy as for hydrogen and likely occurs significantly later and as a result of a different process (see, e.g., 6.3.2 of Barkana and Loeb 4). For this thesis, we focus § exclusively on hydrogen ionization, and the single ionization of helium, and treat the term “reionization” as being synonymous with this. To help understand where reionization fits into the evolution of the Universe as a whole, we can refer to Figure 1.1, which shows the qualitative evolution of the Universe starting with inflation and the CMB on the far left and ending with the present-day Universe on the right and spanning 13.8 billion years. One of the exciting aspects of reionization is ∼ 1This is ∼ 3 × 10−3% of its current age. If the Universe were an 80-year-old human, then the CMB would provide a picture of him/her when they were less than a day old. 2This was inferred from the lack of Ly α absorption in quasar spectra. However, when this was first observed in 1965, it was not obvious that this was indicative of an ionized IGM rather than a scenario where galaxy formation was so efficient as to remove almost all of the gas from the IGM. See Meiksin (115) for a nice review of the physics of the IGM.
2 1.1 Cosmic Context
Figure 1.1: Milestones in the evolution of the Universe from the Big Bang to today.(Photo from NASA WMAP science team)
3 1.1 Cosmic Context
that so little about it is known for sure. However, a reasonable round-number placement of reionization in this figure would be that it was an extended process that occurred somewhere between 200 million years after the Big Bang and 1 billion years after the Big Bang, likely ∼ coinciding with the formation of the first galaxies. The manner in which reionization progressed is also not known for sure and depends on the specifics of what energetic process is at its root. For example, if “softer” sources, emitting ionizing radiation in the UV but not X-ray, drove reionization, then these photons will see a relatively high photoionization cross section and will not travel far before ionizing hydrogen in their path. Under this scenario, the state of the Universe during reionization would likely resemble a two-phase medium with ionized regions surrounding the ionizing sources and sharp boundaries between the ionized regions and the neutral IGM. Eventually, as the ionized regions grew, they would overlap until the entire volume of the IGM became filled with ionized gas. This is the expected course for reionization in the event that it is driven by the first galaxies. If the ionizing sources mostly have a “harder” spectrum, emitting ionizing radiation strongly in X-ray, then the photoionization cross section of these photons will be relatively low. This is because, for photons with E 13.6eV, the cross section falls off as σ 1/ν3. γ ≫ ∼ Because of this, ionizing radiation from these sources will travel farther on average before ionizing a hydrogen atom. This will result in transitions between fully-ionized regions and fully-neutral regions being more gradual. This is the expected scenario in the case where reionization is driven by X-ray binaries or quasars. Figure 1.2 shows examples slices through numerical simulations of reionization that illustrate how it may have proceeded across cosmic time. The ionized regions in the figure (in white) show how ionized “bubbles” form around galaxies and how they grow and merge to fill progressively more of the IGM. Eventually, the entire volume of the IGM is filled with ionized gas. The figure also illustrates one of the ways in which the size of the ionized regions depends on the properties of the ionizing sources. The fraction of the IGM volume that is
4 1.1 Cosmic Context
in the neutral phase (dubbed the neutral fraction, denoted x ) is fixed and decreases for h HIi lower rows. In each column, the ionizing luminosity of a galaxy is assumed to be a power law in the mass of the galaxy’s host dark matter halo, with the typical host halo mas increasing as one moves from left to right. As such, the rightmost column demonstrates a plausible reionization scenario when very rare and massive sources dominate the ionizing photon budget. We can see this results in larger ionized regions for a fixed neutral fraction and sharper boundaries between the neutral and ionized regions. On the other hand, the left- hand columns correspond to a relatively larger contribution to the ionizing photon budget from less-massive sources. The result is a more homogeneous ionization with the ionized regions being smaller, on average. With this qualitative picture in mind, we briefly discuss the broad ways in which reion- ization is important for our understanding of astrophysics and cosmology. First, the Epoch of Reionization is a significant missing piece in the story of the evolution of the Universe and represents a period in the history of the Universe where we have very few direct ob- servations. Work towards understanding reionization is in line with the overarching goal of pushing observations further and further back in time. Second, the Epoch of Reioniza- tion marks the time when radiation from luminous sources became the dominant influence on the IGM and understanding the source of this radiation is interesting in its own right. Understanding the evolution in the properties and number of these bright sources is essen- tial for complete cosmological models. Additionally, while the best guess for the source of the ionizing radiation is dwarf galaxies, it is possible that reionization studies will reveal more exotic and unexpected scenarios. For example, annihilating or decaying dark mat- ter might play a role in reionizing the Universe (e.g., Kasuya and Kawasaki 77, Mapelli et al. 100, Pierpaoli 144). Third, the temperature and ionization state of the gas in the Universe plays a regulatory role in galaxy formation: hot and ionized gas will take longer to cool and collapse than cold neutral gas. Since reionization significantly affects both the temperature and ionization state of the gas, understanding reionization will be essential for
5 1.1 Cosmic Context
S2 S1 S3 S4 z = 7.7 z = 7.3 z = 8.7
Figure 1.2: Slices through numerical simulations of reionization. The above panels are simu- lation outputs from McQuinn et al. (109) showing four different reionization models. Neutral regions are shown in black and ionized regions are shown in white. Each row is at fixed xHI h i with xHI =0.8 (top), 0.5 (middle), 0.3 (bottom). The luminosities of the ionizing sources are h i related to their mass by N˙ m1/3 (left), N˙ m (left-middle), N˙ m5/3 (right-middle), and ∝ ∝ ∝ N˙ m but with a larger minimum mass (right). Each slice has a sidelength of L = 93 Mpc. ∝
6 1.2 The Shoulders of Giants
understanding subsequent galaxy formation. Consequently, a key goal of modern cosmology is to understand the timing and nature of reionization. When did it happen? How long did it take? What were the ionizing sources? What were the properties of the ionized regions and how did they evolve? These are the questions we aim to examine in this work.
1.2 The Shoulders of Giants
Before we continue, it is first worth appreciating the difficulty of what we are trying to do. Essentially, we care about measuring the properties of the intergalactic gas – not stars or galaxies – when the Universe was only .1 billion years old, a seemingly impossible task. Fortunately, we are given the invaluable gift that light travels at a finite speed and, as such, if we look at distant objects, we see them as they were in the past. Therefore, if we look at the at the gas between galaxies 13 billion light years away from us, we will see ∼ it as it was roughly 13 billion years ago, when the Universe was only 1 billion years old. This means that, in principle, this information of how the young IGM evolved is directly available to us. However, even taking this into account, the intergalactic gas we care about is not bright and it is located extremely far away, so how are we supposed to observe it? An inspiring aspect of studying the Epoch of Reionization is that – even though it seems impossible to understand the properties of the Universe at such early times – a number of powerful approaches have been developed to determine the nature of reionization. It is this impressive body of work that we aim to build upon. We discuss a selection of the existing and future methods for constraining the EoR in this chapter in order to provide some context and motivation for our work.
1.2.1 The Ly α Forest
Arguably the most powerful tool for constraining the high-redshift IGM to date has been the Ly α forest. This refers to the pattern of absorption lines seen in the spectra of distant
7 1.2 The Shoulders of Giants
bright objects due to intervening hydrogen, as we will discuss. The Ly α forest results, in part, from another invaluable gift to the field of cosmology: the redshifting of light. This redshifting is a consequence of the expansion of the Universe: the wavelengths of photons propagating through the Universe are stretched as the Universe expands. The stretch is seen as a shift in the spectra of distant sources and the precise amount of the shift can be used to infer a cosmological distance to the source via a model for the expansion history of the Universe. Because of this relationship, distances to objects are often measured as a redshift, defined as the fractional increase in wavelength that a photon experiences when travelling from a given distance to us. This is denoted by z and defined according to the expression:
λobserved = λemitted(1 + zemitter). (1.1)
The Ly α forest is seen in the spectrum of extremely bright background objects, usually quasars or gamma-ray burst (GRB) afterglows, after their light has been processed by the intervening gas. Since the intervening gas is primarily composed of hydrogen and since this hydrogen is generally in the ground state, any intervening neutral patches will absorb light from the background object at the Lyman-series wavelengths, with the strongest absorption occurring at the Ly α wavelength: λα = 1216A.˚ If the Universe were not expanding, then all intervening neutral hydrogen would absorb light from the quasar at one wavelength:
λα = 1216A,˚ neglecting the other lines in the Lyman-series for the moment. However, due to the expansion of the Universe, photons emitted from the quasar/GRB blueward of the Ly α line will redshift as they travel towards us. If they encounter neutral hydrogen as they redshift through the Ly α line, then they will be absorbed and an absorption line will be seen in the spectrum of the background quasar at a wavelength blueward of Ly α (in the rest frame of the quasar/GRB). This process is sketched in Figure 1.3. Thus, the Ly α forest is the pattern of absorption lines seen blueward of the rest-frame Ly α line in quasar spectra due to intervening neutral gas.
8 1.2 The Shoulders of Giants
The same logical progression also applies to the other lines in the Lyman-series. There- fore, you could imagine observing a Ly β and Ly γ forest at smaller wavelengths. There are a couple differences, however. First, lines deeper in the series have a smaller cross section for absorption, so intervening hydrogen will absorb less at these frequencies. Second, photons emitted from a background source with energies larger than Ly β will redshift through the Ly β wavelength and also possibly through the Ly α wavelength before reaching us and will have two opportunities to be absorbed. The photon’s physical location when it redshifts through those two wavelengths will be completely different and, therefore, when observing absorption lines in the Ly β forest, it can be difficult to tell if the photons were absorbed by distant gas undergoing a Ly β transmission or closer gas undergoing a Ly α transition. This problem is clearly exacerbated when considering still higher-order lines since a larger number of distinct regions along the line of sight can contribute to the absorption. We show two example quasar spectra in Figure 1.4. The spectrum in the top panel is for a quasar at relatively low redshift and shows very little absorption. Meanwhile, the quasar in the bottom panel shows little absorption for emitted wavelengths redward of Ly α but is heavily punctuated by absorption blueward of Ly α due to intervening neutral hydrogen. At this point, the Ly α forest should sound like a perfect tool: if we want to map the distribution of neutral hydrogen along the line of sight to a distant bright source, we can simply map each absorption line in the Ly α forest to a parcel of neutral hydrogen. However, the story becomes complicated here due to the extremely great tendency for hydrogen atoms to absorb at the Ly α wavelength. The tendency for absorption by a parcel of gas is typically quantified by an “optical depth”, denoted τ. The fraction of light incident on the cloud that emerges unabsorbed, F , is related to the optical depth by
F = e−τ . (1.2)
The optical depth for Ly α absorption of a neutral hydrogen gas parcel is approximately
9 1.2 The Shoulders of Giants
1+ z 3/2 τ 3.3 104x (1 + δ) (1.3) α ≈ × HI 6.5 where x is the fraction of the hydrogen in the cloud that is neutral and δ (ρ HI ≡ − ρ¯)/ρ¯ is the local baryonic overdensity in units of the cosmic mean. We approximate the line profile of the transition as a delta function in frequency here, but we discuss more realistic descriptions of the line profile in 1.2.1.3 and 1.2.1.4. Using this expression, we § § can calculate the minimum neutral fraction needed for a gas parcel at mean density to allow 1% transmission at z = 5.5:
.01 = e−τmin = τ 4.6 (1.4) ⇒ min ≈ 4.6 τ x (1.5) ≈ α HI,min = x 1.4 10−4. (1.6) ⇒ HI,min ≈ × This reveals the fly in the ointment here: even a gas parcel that is 99.9% ionized will allow less than 1% transmission at the redshifts of interest for reionization. Evidently, even highly-ionized gas can lead to near complete absorption in the Ly α line at the redshifts of interest. Therefore, we can not simply map absorption lines in the Ly α forest to regions of significantly-neutral hydrogen. In fact, the second example quasar we see in Figure 1.4 shows significant Ly α absorption and is located at z = 3.62, much later than the end of reionization. The idea that absorption lines in the Ly α forest correspond to isolated parcels of neutral hydrogen is a useful tool in explaining the basic idea here, but is actually quite inaccurate. Instead, it is more accurate to say that absorption in the Ly α forest traces fluctuations in the underlying density field along the line of sight (Croft et al. 39). At the redshifts that we are concerned with, the density of the IGM is such that the forest is significantly more absorbed than shown in Figure 1.4, with isolated absorption lines becoming exceedingly rare.
10 1.2 The Shoulders of Giants
At this point, the reader may ask what utility does the Ly α forest have at all? Well, an enormous amount. With the fluctuating pattern of transmission and absorption in the Ly α forest in part tracing line-of-sight fluctuations in the underlying matter distribution, we are able to use it to constrain the matter power spectrum, measure baryon acoustic oscillations, and put lower limits on the mass of the dark matter (Viel et al. 178), for example. Additionally, absorption features due to damped Ly α absorbers (DLAs) can be used to measure the primordial deuterium abundance as a test of big bang nucleosynthesis. suspense! But how to constrain the EoR?
11 1.2 The Shoulders of Giants
Figure 1.3: Illustration of the basic physics behind the Ly α forest and how gas at different locations along the line of sight results in absorption lines at different wavelengths. (Image from http://www.astro.ucla.edu/)
12 1.2 The Shoulders of Giants
Figure 1.4: Flux as a function of rest-frame wavelength for a quasar at z = 0.158 (top) and z = 3.62 (bottom). The denser IGM at higher z results in a dense “forest” of ab- sorption lines blueward of the rest-frame Ly α line (1216A)˚ in the lower panel. (Image from http://www.astro.ucla.edu/)
13 1.2 The Shoulders of Giants
1.2.1.1 Evolution of τeff
Perhaps the most common analysis performed on high-redshift quasar spectra in the context of constraining the EoR is measurements of the effective Gunn-Peterson optical depth, defined as
F e−τeff (1.7) h i≡ where F is the averaged transmission fraction over a redshift bin in a quasar/GRB spec- h i trum. Under the assumption of a uniform ionizing background and ionization equilibrium, where the rate that neutral hydrogen atoms are ionized is equal to the rate that ionized hydrogen atoms recombine, the effective optical depth encodes important information about the state of the IGM. In order to see this, we can take a few steps to express the optical depth in terms of the properties of the IGM.1 First, the Gunn-Peterson optical depth can be expressed as
2 πe nHI τGP = fαλα , (1.8) mec H(z)
where H(z) is the Hubble parameter at redshift z, e is the charge of the electron, me
is the electron mass, c is the speed of light, λα is the Ly α wavelength, fα is the quantum mechanical oscillator strength, and nHI is the number density of neutral hydrogen atoms. All of these quantities are known with the exception of the number density of neutral hydrogen atoms. To find this, we first utilize the statement of ionization equilibrium:
1The following discussion will borrow heavily from Faucher-Giguere et al. (53) and Fan et al. (49).
14 1.2 The Shoulders of Giants
ΓHInHI = R(T )nenHII (1.9)
R(T )nenHII nHI = (1.10) ΓHI R(T )ne xHI = (1.11) ΓHI
where ΓHI is the photoionization rate due to the ionizing sources, ne is the number density of free electrons, nHII is the number density of ionized hydrogen atoms (protons),
and xHI is the hydrogen neutral fraction. The left-hand side of Eq. 1.9 represents the rate of photoionizations per volume and the right hand side represents the rate of hydrogen recombinations per volume. Under the assumption of ionization equilibrium with a uniform ionizing background, the presence of any transmission suggests n n + n = n and HII ≈ HI HII H
2 ρc(z)Ωb(z)(1 YHe) 3H (z) Ωb(z)(1 YHe) n¯H = − = − (1.12) mp 8πG mp 3H2Ω (1 Y ) = 0 b,0 − He (1 + z)3 (1.13) 8πG mp
nH = (1+ δ)¯nH. (1.14)
In this expression, ρc is the critical density for a flat Universe, Ωb is the baryon density
in units of the critical density, YHe is the fraction of baryonic mass in the form of helium such that (1 Y ) is the fraction of baryonic mass in the form of hydrogen, and m is the − He p mass of the proton which is effectively equal to the mass of the hydrogen atom. A subscript
of “0” denotes that these are present-day values andn ¯H denotes the average of nH. Thus, as we expect, this expression is essentially equal to the mass density of hydrogen atoms in the Universe divided by the mass per atom.1 The expression for the electron number
1It may be interesting to note that this value corresponds to 0.2 hydrogen atoms per cubic meter today and roughly ∼50 hydrogen atoms per cubic meter at z = 5.5. It is very empty out there.
15 1.2 The Shoulders of Giants
density should be the same, since each ionized hydrogen atom releases one free electron. However, provided helium is singly-ionized along with hydrogen, the number density will increase according to:
3H2 (1 Y ) Y n¯ =n ¯ +n ¯ = − He + He (1.15) e H He 8πG m 4m p p 1.08¯n . (1.16) ≈ H For simplicity in this discussion, but not in the body of this thesis, let us approximate n n n . The quantity R(T ) in Eq. 1.9 is the recombination rate, which is equal to tot ≡ e ≈ H (Hui and Gnedin 72):
T −0.7 R(T ) 4.2 10−13 cm3 sec−1 . (1.17) ≈ × 104K For δ . 5, Hui and Gnedin (72) showed that the temperature and density follow the relationship
T T (1 + δ)γ−1 (1.18) ≈ 0
where T0 is the temperature of a parcel of gas at mean density, and γ is the slope of the temperature-density relation. This tight relationship will become less accurate as one approaches reionization, as we discuss in 4. For compactness, let’s define R R(T = § 4 ≡ 104K). At this point, we are ready to combine Eq. 1.18, 1.17, 1.14, 1.10, and 1.8 to get an expression for τGP:
2 −0.7(γ−1) 2 2 πe fαλα R4(1 + δ) n¯tot(z)(1 + δ) τGP = (1.19) mec H(z) ΓHI πe2 f λ R n¯2 (z) = α α 4 tot (1 + δ)2−0.7(γ−1). (1.20) mec H(z) ΓHI
16 1.2 The Shoulders of Giants
Finally, we have an expression for the Ly α optical depth in terms of several properties of the IGM. The primary unknown in the above expression is the photoionization rate, which is a very complicated parameter that depends on the number, intensity, spectrum, and prox- imity of ionizing sources among other things. In most previous work, the photoionization rate has been approximated as spatially uniform. This approximation is well-motivated at z 5 or so, when the mean free path to ionization photons is inferred to be rather ≤ long (e.g., Prochaska et al. 149, Worseck et al. 183). At these redshifts, each gas parcel is exposed to ionizing radiation from many sources and so fluctuations in the radiation field are correspondingly small. During reionization, however, the photoionization rate will have large spatial fluctuations: there will be neutral regions that have not yet been exposed to radiation, and even the radiation field incident on ionized parcels will vary with the size of the ionized region that the parcel belongs to, and on other IGM properties. Regardless, with this approximation, the observed mean transmission in a region of the spectrum is akin to an average of Eq. 1.20 marginalizing over the density field:
F = dδ e−τ(δ)P (δ) e−τeff , (1.21) h i ≡ Z where we substitute our expression in Eq. 1.20 for τ(δ) above. It is then interesting to adopt a model for the probability distribution of the underlying density field (extracted from numerical simulations of cosmological structure formation), and determine the value of Γ (assumed to be uniform) that matches the observed mean flux, F . With estimates HI h i of the photoionization rate in hand, we can utilize Eq. 1.11 in order to obtain measurements of the IGM neutral fraction in each redshift bin, thus providing us with a handle on the progress of the EoR. Results for measurements of Γ and x via this method, performed HI h HIi by Fan et al. (50), are shown in Figure 1.5. This figure demonstrates that, using τeff and the assumption of ionization equilibrium with a uniform ΓHI, estimates of the neutral fraction are exceedingly small for z . 6. This argument has played a large part in forming the common knowledge that reionization has ended by z = 6.
17 1.2 The Shoulders of Giants
Figure 1.5: The inferred evolution of the photoionization rate, ΓHI (left), and neutral fraction (right) from Fan et al. (50). In the left-hand panel, measurements of the effective optical depth in the Ly α (blue), Ly β (green), and Lyγ (magenta) forest are converted to estimates of the photoionization rate, with arrows indicating upper bounds. The small circles are measurements in individual redshift bins over the 19 quasars used with the large circles being averages. In the right-hand panel, measurements of the photoionization rate are converted to estimates of the volume-averaged neutral fraction.
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Despite the widespread analysis of τeff in constraining the end of reionization, the inter- 1 pretation of τeff is quite complicated. In particular, assuming that the ionization state of the IGM is determined by a spatially-uniform ΓHI is tantamount to assuming that reioniza- tion has, in fact, completed. Specifically, as discussed in 1.1, reionization is likely a highly § inhomogeneous process with ionized bubbles forming around the brightest sources, growing, and eventually overlapping. During the period prior to complete overlap, regions of neutral hydrogen will be shielded from the ionizing radiation while ionized bubbles will experience
a very large ΓHI. This is not reflected in Eq. 1.9 and so we expect conclusions derived from this method to be unreliable when we begin to push up against the end of reionization.
1For a more thorough discussion of controversial aspects of these constraints, see the intro to McGreer et al. (105).
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1.2.1.2 Dark Pixel Covering Fraction
As demonstrated in the previous section, interpreting measurements of the effective optical depth in the context of reionization is complicated and can rely on controversial assumptions. However, an alternative approach is to consider what constraints can be made without resorting to such assumptions. In this regard, measurements of the dark pixel covering fraction in high redshift quasars can be used to place robust upper limits on the fraction of the IGM volume that is in the neutral phase, x . This approach is rooted in the fact h HIi that neutral parcels of gas are certain to result in saturated absorption in quasar spectra 4 due to their optical depths being τHI & 10 (Eq. 1.8). Therefore, a reliable upper bound on the neutral fraction at a given redshift can be estimated by the fraction of pixels in quasar spectra that are completely absorbed at that redshift. An obvious drawback of this method is that, at z 6, overdense yet ionized regions will ∼ also result in saturated absorption and may significantly increase this upper bound on the neutral fraction. One approach to combat this effect is to incorporate the Ly β forest into the analysis. The optical depth for Lyman-series transitions scales as fλ, where f is the oscillator strength of the transition and λ is the corresponding wavelength. Therefore, the analogous expression of Eq. 1.8 for Ly β is:
f λ 1+ z 3/2 τ = τ β β 5.3 103x (1 + δ) . (1.22) β α × f λ ≈ × HI 6.5 α α
where fα = 0.4162, λα = 1216A,˚ fβ = 0.0791, and λβ = 1026A.˚ From this expression, we can see that a mean-density parcel of neutral gas should cause saturated absorption in both the Ly α and Ly β transitions. Meanwhile, ionized overdense regions are less likely to cause saturated absorption as their optical depth in Ly β is reduced by a factor of f λ /f λ β β α α ≈ 1/6. Therefore, limits from the dark-pixel covering fraction may be improved by requiring simultaneous absorption in both Ly α and Ly β as part of the definition of a dark pixel. Additionally, the Ly β dark pixel covering fraction on its own is a viable tool for establishing
20 1.2 The Shoulders of Giants
an upper bound on the neutral fraction, although foreground Ly α absorption may undo some of the gains from the lower τβ value. In practice, all three approaches (requiring Ly α, Ly β, and Ly α+Ly β absorption) are used. This procedure faces several complications when actually carried out, however. First, there are several sources of random noise that add scatter to each observed quasar spectrum. This can result in spurious transmission in pixels that otherwise would have been completely absorbed. Therefore, to measure the dark pixel fraction in quasar spectra, one first needs to create a suitable definition of what qualifies as a “dark” pixel. One approach here is to define dark pixels as having transmission below some threshold defined in terms of the noise standard deviation, σN. This presents us with a trade-off, however, since larger thresholds will reduce the number of neutral pixels we miss but also increase the number of ionized pixels that get incorporated into the dark pixel population. Alternatively – provided the noise has zero median – half of all truly-absorbed pixels will result in negative flux values, on average. This presents the possibility of using twice the negative-flux pixel covering fraction as an estimate of the dark-pixel covering fraction (or four times, in the case of requiring Ly α+Ly β absorption) (McGreer et al. 104). A second complication is that, since pixels have a finite width, their transmission val- ues effectively represent an average of the transmission over some region in the spectra. If the pixel width is large enough, then it is possible for a pixel to have non-zero trans- mission despite corresponding to a physical region that contains significantly-neutral gas. For example, if the physical region in space associated with the pixel is 80% composed of completely-neutral gas and 20% composed of completely ionized gas which allows full trans- mission, then the transmission of that pixel will be 20% and will likely not qualify as a “dark pixel” despite containing neutral gas. Thus, even in a measurement as seemingly-simple as the dark-pixel covering fraction, these details must be kept in mind when interpreting results.
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Regardless, McGreer et al. (105) and McGreer et al. (104) apply the dark-pixel covering fraction approach to 22 high-redshift quasar spectra to produce the constraints on x h HIi shown in Figure 1.6. Dimly-colored points correspond to McGreer et al. (105) while bold- colored points correspond to McGreer et al. (104). These results present a very different interpretation than using τeff measurements while using the same data. Namely, this model- independent analysis does not in fact require reionization to complete by z . 6, contrary to much of the conventional wisdom in the reionization field.
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1.0
0.8
0.6 HI ¯ x 0.4
0.2
0.0 5.2 5.4 5.6 5.8 6.0 z
Figure 1.6: Current limits on xHI derived from the dark-pixel covering fraction in McGreer h i et al. (104). Lightly-shaded points are older limits obtained in McGreer et al. (105).
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1.2.1.3 Damping Wing Redward of Ly α
Much of the difficulties in using the Ly α forest to constrain the timing of the EoR can be boiled down to the following problem: interpreting Ly α absorption in high-redshift quasar spectra is difficult because both neutral and ionized gas can result in saturated absorption. Therefore, it is worth asking if there are any ways to break this degeneracy in Ly α absorption in order to determine which absorption is likely due to neutral hydrogen. One potential approach toward this goal, which has received much attention (e.g., Miralda- Escude 122, Chornock et al. 34, Chornock et al. 33, Mortlock et al. 129, Bolton et al. 21), is looking for the hydrogen damping wing redward of the Ly α line. To understand this approach, let us first understand what the hydrogen damping wing is. For many applications, it is suitable to consider an atom’s ability to absorb radiation as a series of delta functions in frequency: when incident radiation has a frequency exactly coinciding with the energy of the transition, then there is a non-zero probability for ab- sorption and zero probability otherwise. In reality, the probability of absorbing a photon of a given frequency, i.e., the line profile, is a continuous distribution which, while small for frequencies ν = ν , is non-zero. 6 0 The intrinsic line profile for the Ly α transition in the hydrogen atom can be seen as arising from the time/energy uncertainty principle, ∆E ∆t & ~. Specifically, the finite · lifetime of the n = 2 excited state implies the existence of a range of energies that can excite, or result from, the transition. The distribution of this range of energies follows a Lorentzian distribution:1
1 Γ/4π2 φ(ν)= (1.23) π (ν ν )2 + (Γ/4π)2 − 0 with the corresponding absorption cross section
1A quantum-mechanical discussion of this result can be found in §5.8 of Sakurai and Napolitano (158). A classical derivation can be found in §3.6 of Rybicki and Lightman (157).
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πe2 σα(ν)= fαφ(ν), (1.24) mec where Γ is the decay rate of the transition. The “damping wing” refers to the σ ∼ 1/(ν ν )2 behavior far from line center. This can be used to break the degeneracy between − 0 HII absorption and HI absorption because the optical depth is so much smaller in the damping wing that, without significantly-neutral gas (optical depth scales with neutral fraction), the optical depth at such frequency separations will not be sufficient to cause absorption. Furthermore, the damping wing has a distinct shape which can be fit for in order to infer the properties of the neutral gas which sources it. For example, in an extended neutral region, the damping wings from the different parts of the cloud will add together to slow the decay of the overall absorption. As such, compact absorbers will have a narrower damping wing than extended absorbers. This aids us in distinguishing absorption owing to neutral hydrogen in the diffuse IGM from that due to compact DLAs. While the damping wing from an isolated neutral region in a sea of fully-ionized, τ = 0 hydrogen would stand out like a sore thumb, in reality absorption from the surrounding dense, yet ionized, gas will punctuate the damping wing with additional absorption features and will make it harder to detect. This makes the prospect of looking for isolated damping wings in typical regions in quasar spectra unappealing. However, photons emitted slightly redward of Ly α cannot be absorbed by dense ionized gas since ionized gas has a negligible optical depth for ν = ν . Neutral hydrogen, on the other hand, will allow absorption to take 6 α place redward of Ly α due to the significant optical depth in the damping wing. Because of this, searches for the damping wing slightly redward of the Ly α line will be able to avoid nuisance absorption from neighboring ionized gas. We show a famous example of a potential damping-wing detection in Figure 1.7, taken from Mortlock et al. (129). This shows a region of the transmission spectrum for a quasar at redshift z = 7.084 (ULAS J1120+0641). The fractional transmission nearby the Ly α line
25 1.2 The Shoulders of Giants
exhibits a gradual recovery from almost complete absorption at λ < λα to almost complete transmission at λ > λα, occurring over a wavelength interval consistent with a hydrogen damping wing. The curves in blue show models for damping wing absorption associated with an IGM with neutral fraction x = 0.1 (top), 0.5 (middle), and 1 (bottom) with h HIi a sharp ionization front at a distance of 2.2Mpc from the quasar. In green, a model for the absorption profile of a Damped Ly α Absorber (DLA, see glossary for definition) with column density N = 4 1020cm−2 located 2.6 Mpc from the quasar is shown. Thus, the HI × transmission profile appears consistent with both a significantly-neutral ( x > 0.1) IGM h HIi or a proximate DLA. However, Simcoe et al. (167) perform a search for metal lines, which typically accompany DLA absorption, and find that the gas is extremely metal-poor. This bolsters the claim that the damping-wing absorption seen in this example is, in fact, due to diffuse neutral hydrogen in the IGM. Other searches for damping-wing absorption redward of Ly α have been carried out on, for example, GRB 130606A (Chornock et al. 34) and GRB 140515A (Chornock et al. 33). These authors looked for the damping wing in the spectra of GRB afterglows at redshift z = 5.913 and z = 6.33, respectively. A non-detection in the spectra of the z = 5.913 GRB allowed the authors to place a 2σ limit on the nearby IGM neutral fraction of x < 0.11. h HIi Similarly, no strong evidence of a damping wing was found in the spectrum of GRB 140515A, shown in Figure 1.8. The right-hand panel shows the transmission fraction nearby the Ly α 18.62 −2 transition, which is equally-well fit by pure host absorption (blue, NHI = 10 cm ), pure IGM absorption from gas at 6.0 z 6.328 with x = 0.056 (red), and a hybrid model ≤ ≤ h HIi with a host absorber lying within an ionized bubble with R = 10 comoving Mpc met by an IGM with x = 0.12 (green). As such, they argue against a significantly-neutral IGM at h HIi this redshift. It is worth pointing out, however, that the method of searching for the damping wing redward of Ly α is not without drawbacks. First, detecting the damping wing redward of Ly α relies on your ability to understand what the quasar flux would have been in the
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Figure 1.7: Quasar ULAS J1120+0641 identified at redshift z =7.085 along with several fits for the damping wing.
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absence of the absorbing gas nearby the Ly α line (this unabsorbed flux is referred to as the quasar continuum and predicting the unabsorbed flux for a given quasar is called continuum fitting). Predicting the Ly α line properties in quasars is notoriously complicated and so modelling the precise fractional transmission must be done with care. Second, searching for the damping wing redward of Ly α inherently involves measuring the gas properties nearby the quasar. However, quasars are extremely rare and special objects and it is not obvious that their surroundings are representative of the IGM on average. For example, Lidz et al. (88) found that quasars are likely born into large galaxy-generated ionized regions, suggesting that interpreting the lack of a damping wing detection is not straightforward. Gamma-ray burst afterglow spectra are gaining attention in this regard (See Salvaterra 159 for a review) as they tend to occupy more typical regions of space and have an easier-to- model continuum flux. The drawbacks of GRBs, though, is that they are often accompanied by a host absorber whose damping-wing absorption must be separated from that of the IGM. Third, even when provided with a clean detection of the damping wing redward of Ly α, this will only tell you about one region of space and it will be difficult to use this single observation to extrapolate to the ionization state of the IGM as a whole. Later in this work, we propose a technique for searching for the hydrogen damping wing which, while faced with its own difficulties, is able to avoid the difficulties mentioned above.
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Redshift of Lyα Rest Wavelength (Å) ) 4.5 5.0 5.5 6.0 6.5 7.0 1210 1220 1230 −1 4 Å ⊕ 1.0 −1 s
−2 3 0.8 GRB 140515A 2 at z=6.327 0.6 erg cm Host only 0.4 −17 1 C IV(z=4.804) Al II IGM only Combined 0.2 , 10 λ
with R =10 Mpc Transmission Fraction 0 b 0.0
Flux (f 7000 8000 9000 10000 8900 9000 Observed Wavelength (Å) Observed Wavelength (Å)
Figure 1.8: Spectrum of GRB140515A, a gamma-ray burst located at z = 6.33. The right- hand panel overlays damping wing models from a host absorber (blue), a pure IGM model with
xHI =0.056 (red), and a combination model (green). The authors argue that, while each curve h i provides an equally-good fit to the data, the sharp rise in transmission shown is inconsistent with a significantly-neutral IGM.
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1.2.1.4 IGM Temperature
A detection of a damping wing redward of the Ly α line in a quasar spectra would con- stitute a “smoking gun” for significantly-neutral regions in the IGM, provided you could rule out the possibility of a DLA source. However, in the absence of a smoking gun, a warm gun could be an indication of reionization having completed recently. Specifically, measurements of the IGM temperature can provide us with additional insights about the process of reionization. The utility of the IGM temperature in studying reionization stems mostly from the long cooling time of the low-density gas. The gradual cooling of the gas implies that it retains some memory of when and how it was ionized. Typically, the gas is photo-heated to temperatures of 20, 000K during reionization. The main cooling mech- ∼ anism is adiabatic cooling from the expansion of the Universe, although Compton cooling off of the CMB is important for gas that is ionized at sufficiently early times, at z & 10 or so. In general, gas that was ionized early on will have longer to cool and will reach a lower temperature sooner than gas that ionized more recently. Since the memory of prior photo-heating gradually fades, this measurement is most powerful if it can be made as close as possible to reionization (e.g., Miralda-Escud´eand Rees 124, Hui and Gnedin 73, Lidz and Malloy 87). Because of this relatively simple cooling behavior, it should be possible to turn a measurement of the temperature of the IGM into a constraint on the timing of reionization. In order to do this, we need two main ingredients: a method of measuring the temperature of high-redshift gas and an understanding of how the temperature of the gas evolves with time after being ionized. One popular method for determining the temperature of the IGM utilizes the width of absorption lines in the Ly α forest. In 1.2.1.3, we described the line profile for Ly α § absorption as obeying a Lorentzian distribution. While this is technically correct for any given atom, in reality, the atoms themselves have random thermal motions according to their temperature and will therefore see incident radiation as being redshifted or blueshifted
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accordingly.1 As such, a hydrogen atom travelling away a photon with frequency just above the Ly α frequency will see the light redshifted and can increase the chance of absorption. The effect of this is that the line profile for Ly α absorption from a gas parcel gets smeared out, or, more precisely, gets convolved the with Maxwell-Boltzmann distribution. The greater the temperature, the greater the extent of this smearing. The Maxwell-Boltzmann distribution describes the velocities of particles in an ideal gas with a given temperature:
1/2 mp 2 W (ξ)dξ = e−mpξ /2kB T dξ (1.25) 2πk T Bs −1/2 2 2 2 −ξ /ξ0 = πξ0 e dξ (1.26)